Properly Discounted Asset Prices Are Semimartingales

Dániel Ágoston Bálint and Martin Schweizer
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Dániel Ágoston Bálint: ETH Zurich - Department of Mathematics
Martin Schweizer: ETH Zurich; Swiss Finance Institute

No 19-53, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We study general undiscounted asset price processes, which are only assumed to be non-negative, adapted and RCLL (but not a priority semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage, the original prices discounted by the value of any simple strategy with positive wealth must follow semimartingales. As a side result, we establish two corresponding versions of the fundamental theorem of asset pricing that involve supermartingale discounters with some additional strict positivity property.

Keywords: semimartingales; discounting; dynamic share viability; simple strategies; noshort-sales constraints; NA1 for simple strategies; supermartingale discounter (search for similar items in EconPapers)
JEL-codes: C00 G10 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2019-10
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1953

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